Enter the matrix: the deep law that shapes our reality

SUPPOSE we had a theory that could explain everything. Not just atoms and quarks but aspects of our everyday lives too. Sound impossible? Perhaps not.

It’s all part of the recent explosion of work in an area of physics known as random matrix theory. Originally developed more than 50 years ago to describe the energy levels of atomic nuclei, the theory is turning up in everything from inflation rates to the behaviour of solids. So much so that many researchers believe that it points to some kind of deep pattern in nature that we don’t yet understand. “It really does feel like the ideas of random matrix theory are somehow buried deep in the heart of nature,” says electrical engineer Raj Nadakuditi of the University of Michigan, Ann Arbor.

All of this, oddly enough, emerged from an effort to turn physicists’ ignorance into an advantage. In 1956, when we knew very little about the internal workings of large, complex atomic nuclei, such as uranium, the Hungarian physicist Eugene Wigner suggested simply guessing.

Quantum theory tells us that atomic nuclei have many discrete energy levels, like unevenly spaced rungs on a ladder. To calculate the spacing between each of the rungs, you would need to know the myriad possible ways the nucleus can hop from one to another, and the probabilities for those events to happen. Wigner didn’t know, so instead he picked numbers at random for the probabilities and arranged them in a square array called a matrix.